W e are also committed to releasing the code. Implementation details for Stage 2. Our implementation strictly follows the previous work that also In this section, we briefly introduce our tasks. It requires the robot hand to open the door on the table. It requires the robot hand to orient the pen to the target orientation. It requires the robot hand to place the object on the table into the mug. We present the success rates of our six task categories as in Table 1.

In this Appendix, we will derive the fixed-point equations for the order parameters presented in the main text, following and generalising the analysis in Ref. [ Saddle-point equations The saddle-point equations are derived straightforwardly from the obtained free energy functionally extremising with respect to all parameters. The zero-regularisation limit of the logistic loss can help us study the separability transition. N 5 + \ 1 p 0, 1 d 5. (66) As a result, given that \ 2( 0, 1 ], the smaller value for which E is finite is U This result has been generalised immediately afterwards by Pesce et al. Ref. [ 59 ] for the Gaussian case, we can obtain the following fixed-point equations, 8 > > > > > >< > > > > > >: E = Mean universality Following Ref. [ In our case, this condition is simpler than in Ref. [ We see that mean-independence in this setting is indeed verified. Numerical experiments Numerical experiments regarding the quadratic loss with ridge regularisation were performed by computing the Moore-Penrose pseudoinverse solution.

The development of efficient machine learning models for molecular systems representation is becoming crucial in scientific research.

We thank the reviewers for the detailed and insightful reviews. As the reviews noted, our work 1) introduces "novel Smith et al. [2017] make an explicit connection between small vs. large batch "A small discussion on if the phenomenon has been observed for different datasets/tasks with different optimizers" The phenomenon may not be true for other optimizers such as Adam, though. "concept of "memorizable and generalizable", though intuitive, is sketchy and not formally explained ... authors We acknowledge that the terms "memorizable" and "generalizable" are potentially confusing. We will revise our terminology to clarify this distinction. By "inherently noisy", we refer to the fact that high noise in the datapoints will necessitate larger sample complexity.